Regarding Multi-Instance Learning as a Denoising Process for Single-Cell Data

Pooling single-cell embeddings into multi-sample bags can improve generalisation to unseen experimental settings. Canonically, bags are formed for convenience, since labelling a bag is cheaper than labelling every instance, and bags are generated the same way during training and at deployment, with instance-level labels free to vary within a bag (Dietterich et al.,1997). Dapello et al. (2025), by contrast, assume bags are constructed with perfect instance level accuracy such that each bag contains samples from the same class during both training and testing. In this work, we show that bag size and bag impurity act through distinct mechanisms. Bag size governs the variance of the mean embedding, with larger bags yielding lower variance, while impurity acts as a bias, shrinking the class-specific bag mean toward a shared centroid. This distinction motivates **Denoising DeepSets (DDS)**, which inserts a noise-conditioned denoiser between mean pooling and classification. By conditioning on the effective noise level implied by bag size, DDS can be trained across bag sizes and can be deployed at any evaluation bag size without retraining. On the datasets from the scGeneScope benchmark, DDS improves on mean-pooling and attention-based MIL baselines with the largest gains at small bag sizes where sampling noise is greatest. These results on both single-cell RNA sequencing and Cell Painting microscopy images suggest that treating bag size as a structured noise variable provides a principled route from bag-level training to robust single-cell prediction.